Solution to: The Prince and the Pearls

The best way is to put one black pearl in the first vase and all other pearls in the second vase. Then, the probability of grabbing a black pearl from the first vase is 1, and the probability of grabbing a black pearl from the second vase is ⁹⁹⁄₁₉₉. The total probability of grabbing a black pearl is ½ × 1 + ½ × ⁹⁹⁄₁₉₉ = ²⁹⁸⁄₃₉₈ (approximately 74.9%).

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